Öncü verinin belirsizliği durumunda biyoçeşitliğin belirlenmesinde Shannon entropisinin Deng entropisi ve geliştirilmiş Deng Entropisi ile karşılaştırılması

Year 2018, Volume: 68 Issue: 2, 136 - 140, 20.07.2018

Kürşad Özkan

Abstract

DOI: 10.26650/forestist.2018.340634

Biyolojik çeşitliliğin belirlenmesinde
Margalef indeksi, McIntosh indeksi, Simpson indeksi, Brillouin indeksi ve
Shannon entropisi gibi birçok çeşitlilik indisi kullanılmaktadırlar. Bu
indisler arasındaki en popular olanı Shannon entropisidir. Bu çalışma biyolojik
çeşitliğin ölçümüne yönelik olarak bilgi teorisinin temel eşitliği olan Shannon
entropis ile Demster-Shafer Delil Teorisi’nin ölçümlerinden olan Deng entropisi
ve Geliştirilmiş Deng entropisini karşılaştırmak için gerçekleştirilmiştir.
Çalışmada 3 kompleksten oluşan hipotetik bir veri kullanılmıştır. Kullanılan
hipotetik veri ile gerçekleştirilen hesaplamaların sonucunda, ekolojik açıdan
en makul sonuçlar Geliştirilmiş Deng entropisi ile elde edilmiştir. Bu sonucun
iki sebebi bulunmaktadır. Birincisi Shannon entropisi hesaplanırken kütle
fonksiyonları kullanılamamaktadır. İkincisi ise Deng entropisinin sezgisel yapı
ölçeğini dikkate almamasıdır.

Keywords

Geliştirilmiş kanaat entropisi, bilgi teorisi, belirsizlik, kütle fonksiyonu, temel olasılık ataması, sezgisel yapı, alfa çeşitliliği

Comparing Shannon entropy with Deng entropy and improved Deng entropy for measuring biodiversity when a priori data is not clear

Abstract

DOI: 10.26650/forestist.2018.340634

The various diversity measures used to
measure biodiversity include the Margalef index, McIntosh index, Simpson index,
Brillouin index, and Shannon entropy. Of these measures, the most popular is
Shannon entropy (H). In this study, with respect to measuring biodiversity, we
compare Shannon entropy-the essential aspect of information theory-with the
Deng and improved Deng entropies, as proposed within the framework of the
Dempster–Shafer evidential theory. To do so, we used a hypothetical dataset of
three complexes. Based on this hypothetic data, ecologically speaking, we
obtained the most reasonable result from the improved Deng entropy. There are
two reasons for this result: 1) Mass functions cannot be used when computing
the Shannon entropy, and 2) Deng entropy does not take into consideration the
scale of the frame of discernment.

Keywords

Improved belief entropy, information theory, uncertainly, mass function, basic probability assignment, frame of discernment, alpha diversity

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